Scale Mixtures of Normal Distributions

SUMMARY This paper presents necessary and sufficient conditions under which a random variable X may be generated as the ratio ZI V where Z and V are independent and Z has a standard normal distribution. This representation is useful in Monte Carlo calculations. It is established that when 7 V2 is exponential, X is double exponential; and that when WV has the asymptotic distribution of the Kolmogorov distance statistic, X is logistic.